In this paper, a generalized $\epsilon-$subdifferential, which was
defined by a norm, is first introduced for a vector valued mapping.
Some existence theorems and the properties of the generalized
$\epsilon-$subdifferential are discussed. A relationship between the
generalized $\epsilon-$subdifferential and a directional derivative
is investigated for a vector valued mapping. Then, the calculus
rules of the generalized $\epsilon-$subdifferential for the sum and
the difference of two vector valued mappings were given. The
positive homogeneity of the generalized $\epsilon-$subdifferential
is also provided. Finally, as applications, necessary and sufficient
optimality conditions are established for vector optimization
problems.

References:

[1]

T. Amahroq, J.-P. Penot and A. Syam, On the subdifferentiability of the difference of two functions and local minimization,, Set-Valued Anal., 16 (2008), 413.
doi: 10.1007/s11228-008-0085-9. Google Scholar

References:

[1]

T. Amahroq, J.-P. Penot and A. Syam, On the subdifferentiability of the difference of two functions and local minimization,, Set-Valued Anal., 16 (2008), 413.
doi: 10.1007/s11228-008-0085-9. Google Scholar